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If a – B = 3 and Ab = 10, Find : A3 – B3. - Mathematics

Sum

If a – b = 3 and ab = 10, find : a3 – b3.

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Solution

a − b = 3

⇒ (a − b)3 = (3)3

⇒ a3 − b3 − 3ab (a − b) = 27

⇒ a3 − b3 − 3×10 (3) = 27

⇒ a3 − b3 − 90 = 27

⇒ a3 − b3 = 27 + 90

⇒ a3 − b3 = 117

Alternative Method :

(a − b)3 = a3 − b3 − 3ab (a − b)

⇒ (3)3 = a3 − b3 − 3×10 (3)

⇒ 27 = a3 − b3 − 90

⇒ 27 + 90 = a3 − b3

⇒ 117 = a3 − b3

⇒ a3 − b3 = 117

Concept: Application of Formulae
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 12 Identities
Exercise 12 (C) | Q 13 | Page 155
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